MinT - Information on Result #671963

Information on Result #671963

Linear OA(32¹⁵, 32832, F₃₂, 5) (dual of [32832, 32817, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32⁰, 1026, F₃₂, 0) (dual of [1026, 1026, 1]-code) (see above)
linear OA(32¹, 1026, F₃₂, 1) (dual of [1026, 1025, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(32¹, 1026, F₃₂, 1) (dual of [1026, 1025, 2]-code) (see above)
linear OA(32¹, 1026, F₃₂, 1) (dual of [1026, 1025, 2]-code) (see above)
linear OA(32³, 1026, F₃₂, 2) (dual of [1026, 1023, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
  - Hamming code H(3,32) [i]
linear OA(32⁹, 1026, F₃₂, 5) (dual of [1026, 1017, 6]-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OA(32², 33, F₃₂, 2) (dual of [33, 31, 3]-code or 33-arc in PG(1,32)), using
    - extended Reedâ€“Solomon code RS_e(31,32) [i]
    - Hamming code H(2,32) [i]
  2. linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
    - a code by Danev and Olsson [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.